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Bunuel
Two boats, traveling at 5 and 10 kms per hour, head directly towards each other. They begin at a distance of 20 kms from each other. How far apart are they (in kms) one minute before they collide?

(A) 1/12
(B) 1/6
(C) 1/4
(D) 1/3
(E) 1/2

Distance traveled in a minute = 15000/60 = 250 m = 1/4 km

IMO C

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Bunuel
Two boats, traveling at 5 and 10 kms per hour, head directly towards each other. They begin at a distance of 20 kms from each other. How far apart are they (in kms) one minute before they collide?

(A) 1/12
(B) 1/6
(C) 1/4
(D) 1/3
(E) 1/2

Notice that the distance between the two boats one minute before they collide is equal to the total distance traveled by the two boats in one minute.

In 1 minute, the boat with speed of 5 km/hr will have traveled 5 x 1/60 = 5/60 km. Similarly, the boat with speed of 10 km/hr will have traveled 10 x 1/60 = 10/60 km in 1 minute. Therefore, 1 minute before they collide, they are 5/60 + 10/60 = 15/60 = 1/4 km apart.

Answer: C
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So,name the two boats.Boat A=5km/hr and Boat B=10km/hr.
We first find the time taken by them to collide.For this we require the concept of relative speed.
Using the relative speeds formula-When two objects move in opposite directions,their relative speeds add up.
We get, Time after which they collided=Distance between them/Relative speed
=20km/(10+5)km/hr=4/3hr=80 mins
Questions says-1 minute before they collided,ie-79 mins.
We find the distance traveled by Boat A and Boat B in 79 mins and subtract it from the total distance.This would give the distance between the two bodies one minute before colliding.

Boat A(Distance traveled in 79mins)=79x5/60=79/12 km
Boat B(Distance traveled in 79mins)=79x10/60=79/6 km

Distance between Boat A and Boat B=20km(Total Distance)-(79/12+79/6)
=20-237/12
=1/4
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